Simplifying Expressions
Simplify 3x+5x
8x
Find the value of x:
x+7=12
x = 5
Solve: 2x+3=x+5
x = 2
x+4 > 7
x > 3
“Seven more than a number is 15.”
Write AND solve the equation.
n+7=15
n=8
Simplify: −2a+7−3a+4
−5a+11
Solve: 3k=15
k = 5
Solve: 3(x−4)=12
Graph on a number line
x = 8
Graph: Closed circle on 8, no arrows
Solve:
3y − 2 ≤ 7
y ≤ 3
A=2b+c
Solve for c
c = A - 2b
Simplify: 4(2y−3)−y
7y−12
Solve: 2x−4=10
x = 7
Solve and write your answer in set notation:
5x+2=3x+10
Bonus: +100 pts for writing it in formal set notation
{x = 4}
Bonus (+100) : { x | x + 4 }
Solve: (x/2)−1 ≥ 4
Graph on a number line.
x ≥ 10
Graph: Closed circle at 10, arrow to the right (→).
Ms. Nguyen's phone plan costs $10 plus $0.20 per text. If her monthly total is $14, how many texts did she send? (include units in your answer)
t = 20 texts
Combine like terms: 5x−2(x+3)+4x
7x−6
Solve: (1/3)y+5=11
y = 18
1. Solve and write as set notation
1/2(x+6)=2x−3
2. How many solutions are there to this equation?
1. {x = 4}
2. one solution
Solve and graph:
5−2x<1
x>2
Graph: Open circle at 2, arrow to the right (→).
A movie theater charges $12 for adults and $8 for children. The total cost for 2 adults and 3 children is $48. Write and solve an equation to find if the total matches the cost.
Yes, it matches.
Combine like terms:
−3(2m−5)+4(m+1)
−2m+19
Solve:
4x−7=3x+8
x = 15
Solve and write the number of solutions in set notation:
4(x−2)+3 = 2x−1+2x−4
4x - 5 = 4x - 5
Set notation: ℝ
When do you flip an inequality sign when solving?
When you are dividing OR multiplying by a negative number
After paying a $50 startup fee, a gym charges $25 per month. Write and solve an equation to find how many months until a total cost of $200.
m = 6 months